Algorithmic Aspects of Acyclic Edge Colorings

Alon, Noga; Zaks, Ayal

doi:10.1007/s00453-001-0093-8

Cited by 45 publications

(30 citation statements)

References 11 publications

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“…The acyclic chromatic number of G introduced in [1], denoted by a(G), is the least number of colors in an acyclic vertex coloring of G. The acyclic edge chromatic number of G, denoted by a (G), is the least number of colors in an acyclic edge coloring of G. In [2], Alon and Zaks proved that determining the acyclic edge chromatic number of an arbitrary graph is an N P -complete problem, even determining if α (G) 3 for an arbitrary graph G.…”

Section: Introductionmentioning

confidence: 99%

Acyclic edge colorings of planar graphs and seriesparallel graphs

Hou

Liu

et al. 2009

Sci. China Ser. A-Math.

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Section: Introductionmentioning

confidence: 99%

Acyclic edge colorings of planar graphs and seriesparallel graphs

Hou

Liu

et al. 2009

Sci. China Ser. A-Math.

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“…Even for the simple and highly structured class of complete graphs, the value of a (G) is still not determined exactly. It has also been shown by Alon and Zaks [3] that determining whether a (G) ≤ 3 is NP-complete for an arbitrary graph G. The vertex version of this problem has also been extensively studied (see [13,8,7]). A generalization of the acyclic edge chromatic number has been studied.…”

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confidence: 96%

Acyclic edge coloring of graphs with maximum degree 4

Basavaraju

Chandran

2009

Journal of Graph Theory

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An acyclic edge coloring of a graph is a proper edge coloring such that there are no bichromatic cycles. The acyclic chromatic index of a graph is the minimum number k such that there is an acyclic edge coloring using k colors and is denoted by a (G). It was conjectured by Alon, Sudakov, and Zaks that for any simple and finite graph G, a (G) ≤ +2, where = (G) denotes the maximum degree of G. We prove the conjecture for connected graphs with (G) ≤ 4, with the additional restriction that m ≤ 2n−1, where n is the number of vertices and m is the number of edges in G.

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“…Even for complete graphs, the acyclic edge chromatic number is still not determined exactly. It has been shown by Alon and Zaks [23] that determining whether a (G) ≤ 3 is NP-complete for an arbitrary graph G. Now, we provide the following open problems. …”

Section: Acyclic Edge Coloringmentioning

confidence: 98%

The method of coloring in graphs and its application

Liu

Hou

2010

J Syst Sci Complex

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Graph coloring has interesting real life applications in optimization and network design. In this paper some new results on the acyclic-edge coloring, f -edge coloring, g-edge cover coloring, (g, f)-coloring and equitable edge-coloring of graphs are introduced. In particular, some new results related to the above colorings obtained by the authors are given. Some new problems and conjectures are presented.

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Algorithmic Aspects of Acyclic Edge Colorings

Abstract: A proper coloring of the edges of a graph G is called acyclic if there is no 2-colored cycle in G.

Cited by 45 publications

References 11 publications

Acyclic edge colorings of planar graphs and seriesparallel graphs

Acyclic edge colorings of planar graphs and seriesparallel graphs

Acyclic edge coloring of graphs with maximum degree 4

The method of coloring in graphs and its application

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